erweitern (1+2x+3x^2)^5

Lösung

erweitern

(1 + 2 x + 3 x^{2})^{5}

243 x^{10} + 810 x^{9} + 1485 x^{8} + 1800 x^{7} + 1590 x^{6} + 1052 x^{5} + 530 x^{4} + 200 x^{3} + 55 x^{2} + 10 x + 1

Schritte zur Lösung

(1 + 2 x + 3 x^{2})^{5}

(1 + 2 x + 3 x^{2})^{5} = (1 + 2 x + 3 x^{2}) (1 + 2 x + 3 x^{2}) (1 + 2 x + 3 x^{2}) (1 + 2 x + 3 x^{2}) (1 + 2 x + 3 x^{2})

= (3 x^{2} + 2 x + 1) (3 x^{2} + 2 x + 1) (3 x^{2} + 2 x + 1) (3 x^{2} + 2 x + 1) (3 x^{2} + 2 x + 1)

Multipliziere aus

(1 + 2 x + 3 x^{2}) (1 + 2 x + 3 x^{2}) (1 + 2 x + 3 x^{2}) (1 + 2 x + 3 x^{2}) (1 + 2 x + 3 x^{2}) : 243 x^{10} + 810 x^{9} + 1485 x^{8} + 1800 x^{7} + 1590 x^{6} + 1052 x^{5} + 530 x^{4} + 200 x^{3} + 55 x^{2} + 10 x + 1

= 243 x^{10} + 810 x^{9} + 1485 x^{8} + 1800 x^{7} + 1590 x^{6} + 1052 x^{5} + 530 x^{4} + 200 x^{3} + 55 x^{2} + 10 x + 1

e x p an d (k + 1)! (k + 2) - 1

e x p an d (1 + x - x^{2})^{5}

e x p an d 16 - 9 y 4

e x p an d e^{2 x (y l n (y) - y)}

e x p an d (x + y - z)^{5}